Basic Geometry(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

BASIC GEOMETRY MCQs

Total Questions : 93 | Page 8 of 10 pages

Question 71.

If the inner rectangle is 8cm x 6 cm. Find the area of the shaded region.

44 cm $^{2}$
34.25 cm $^{2}$
32.50 cm $^{2}$
None of these

Discuss Question

Answer: Option D. -> None of these
:
D

Diagonal of rectangle: $\sqrt{(8^{2} + 6^{2})}$ , =10.

Half of diagonal = radius of circle = 5.

Area of shaded region: $π$ 5 $^{2}$ - (8x6) = 30.57

Question 72.

The top of a conical container has a circumference of 308 m. Water flows in at a rate of 12 m $^{3}$ every 2 secs. When will the container be half filled, if its depth is 12m.

42 min
68 min
54 min
82 min

Discuss Question

Answer: Option A. -> 42 min
:
A

Ans:a 2 $π$ r=308 2 $\times$ $(\frac{22}{7}) \times r$ = 308 Find half volume of conical container.

Time reqd: $\frac{v o l o f \frac{1}{2} c o n t a i n e r}{f l o w r a t e}$ = $\frac{15078.28}{6}$ = 2520; $\frac{2520}{60}$ =42min

Question 73.

In the figure find the area outside the trapezium, given square is of side 16 cm.

128 cm $^{2}$
154 cm $^{2}$
168 cm $^{2}$
28 cm $^{2}$

Discuss Question

Answer: Option A. -> 128 cm

^{2}

:
A

Required Area = Area of triangle AFG + Area of triangle DEF + Area of triangle BCD =

$(\frac{1}{2} \times 6 \times 8) + (\frac{1}{2} \times 8 \times 6) + (\frac{1}{2} \times 10 \times 16)$

= 128 cm $^{2}$

Question 74.

A well is dug 20 ft deep and the mud which came out is used to build a wall of width 1 ft around the well on the ground. If the height of the wall around the well is 5 ft, then what is the radius of the well?

$\sqrt{5}$
1
$\frac{1}{4}$
$\frac{(\sqrt{5} + 1)}{4}$

Discuss Question

Answer: Option D. ->

\frac{(\sqrt{5} + 1)}{4}

:
D

Solution: - Let radius = r feet.

Volume of mud from well: πr $^{2}$ (20) cubic feet.

Volume of wall around well: 5π((r+1) $^{2}$ -r $^{2}$ ).

πr $^{2}$ (20) = 5π((r+1) $^{2}$ -r $^{2}$ ) => 4r $^{2}$ - 2r - 1=0 $\Rightarrow$ r = $\frac{(\sqrt{5} + 1)}{4}$

Question 75.

A rectangular field is of dimension 15.4m x12.1 m. A circular well of 0.7 m radius and 3 m depth is dug in the field. The mud, dug out from the well, is spread in the field. By how much would the level of the field rise?

1 cm
2.5 cm
3.5 cm
4 cm

Discuss Question

Answer: Option B. -> 2.5 cm
:
B

Solution: - Volume of earth taken out: $π$ r $^{2}$ h. = $π$ x (0.7) $^{2}$ x 3 = V.

Area of field without circle: (15.4x12.1)-( $π$ (0.7 $^{2}$ )) = A (say).

Axh=V

h=2.5 cm

Question 76.

There is an equilateral triangle of side ‘a’ units. Now we join any two sides of the triangle to form a cone.What is the slant height of the cone formed?

$\frac{a}{2 π}$
a
$\frac{a}{2}$
2 $π$ a

Discuss Question

Answer: Option B. -> a
:
B

The cone will have slant height same as the triangle side.

Question 77.

There is an equilateral triangle of side ‘a’ units. Now we join any two sides of the triangle to form a cone.What is the radius of the cone formed?

a
$\frac{a}{4}$
$\frac{a}{π}$
None of these

Discuss Question

Answer: Option D. -> None of these
:
D

Circumfrence of the base of cone = 2 $π$ r = side of triangle = a

radius (r) = $\frac{a}{2 π}$

Question 78.

Sixteen cylindrical sprite cans are placed in a square carton such that each can either touches another can or a wall of the carton. Each can is of unit radius. What is the bottom area of the carton?

16 sq units
64 sq units
32 sq units
None

Discuss Question

Answer: Option B. -> 64 sq units
:
B

Ans: b (Add the radii of cans in 1 row. We get 8 as length. Same for breadth. So, carton dimensions: 8 by 8. Bottom area: 8x8=64 sq units.)

Question 79.

Areas of three adjacent sides of a cuboid are a,b,c. Volume of the cuboid is N. The value of N $^{2}$ equals to?

abc
(ab+ac+bc)
$\sqrt{(a^{3} + b^{3} + c^{3})}$
None of these

Discuss Question

Answer: Option A. -> abc
:
A

Assume sides to be x,y,z. Then xy=a, yz=b, xz=c.

Multiplying: (xyz) $^{2}$ = abc; =N $^{2}$ . (Vol=xyz)

Hence Ans: (a)

Question 80.

A string of certain length n makes one perfect turn around a cube of side A, starting from corner X and ending at Y (as in the fig). Find the length of the string.